By Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau
The lately proposed, absolutely multi-scale idea of doublet mechanics, offered right here in a self-contained shape, bargains unprecented possibilities to reconcile the discrete and continuum representations of solids whereas retaining an easy analytical structure and entire compatibility with lattice dynamics and continuum mechanics. Its purposes contain micro-electro-mechanical structures (MEMS), granular and particulate media, nanotubes and peptide arrays. Novel effects are mentioned, together with the id of a brand new type of dispersive floor waves, and the presentation of equipment for the experimental selection of the basic microstructural parameters. The relationships among doublet mechanics, lattice dynamics, and continuum theories are tested.
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Additional resources for Advances in Doublet Mechanics
Granik and A. Imam) As discussed in Sect. 3, doublet mechanical analysis has been applied to crystalline solids, as well as granular, particulate, and composite media in the past. An exciting novel vista on the applications of the method is offered in Chap. 10 where Chopra and Zettl review the field of nanotubes. Nanotubes are technological objects of extraordinary interest. They are particularly suitable for doublet mechanical analysis because their discrete nature is evident at the structural scale and, as a result, they are not amenable to being modeled as continuous media.
Substituting /::::"u o from eqn. 5) into eqn. 11) and using eqns. , xk 1 ' ••• ,Xk". Each subscript of the set k1 , ••• ,kx runs through the integers 1,2,3. It should be noted that the elongation microstrain fa of the doublet (A, B o ) is caused by the motion of the node bo E B o away from node a E A along the vector To. Therefore, this microstrain can be conveniently represented as €o = fa To. In the above discussion, it was assumed that 1/::::"Ua 1« "10 and fa « 1. , tPo « 1 (see Fig. 4). 13) where foj == fa T~j.
Structures have the valence n = 3 and n = 6, respectively (see Figs. 3). The FCCS is also called pyramidal. For Bravais lattices the bundle Tm (a) admits a decomposition into two disjoint subsets T: (a) and T; (a) which are equivalent via the center of r. 4 Microstructure, Measures of Deformations, Field Equations A Fig. 1. Particle doublet (A, B cr ). A-A Fig. 2. Simple cubic structure (SCS). 15 16 1. Introduction (M. Ferrari, V. T. Granik and A. Imam) B-B Fig. 3. Face-centered cubic structure (FCCS).
Advances in Doublet Mechanics by Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau